where \(a,\,b \,\in \, \Omega ^1(\Sigma ) \otimes \mathfrak {g}\)  are flat \(G\) -connections on \(\Sigma .\) 
For general \(G\) ,
the symplectic form of this space also has this form (see Section 5.2 of
[1]}).
This is
a simple generalization of the symplectic form defined by
Atiyah and Bott [2]}.
